The ratio between a two-digit number and the sum of the digits of that number is 4:1. If the digit in the unit place is 3 more than the digit in the ten's place, what is that number?

36

Let us assume that digits of the number are x and y with x on ten's place.

∴ Number is 10x+y

Given that, digit on unit's place is 3 more than ten's place, i.e. y=x+3 ......(1)

Also, According to the question, 10x + y : x + y = 4 : 1

⇒10x+y = 4x+4y

⇒ y = 2x

Substituting in (1), we get 2x = x+3

∴x = 3, y = 6

The number is 36.

Or, the simplest way of doing these types of question is using "OPTION"

Options are:

24, 63, 36

According to the question,

Number : sum of digits = 4: 1 and 

the digit in the unit place is 3 more than the digit in the ten's place.

Option 1 and 2 are eliminated as it does not fulfill the 2nd condition which states that the unit place must be 3 more than the digit in the ten's place. We are left with 36. It follows the 2nd condition and also the 1st condition which states that the ratio of number : sum = 4 : 1 i.e. 36 : 9 = 4 : 1

Therefore, 36 is the answer.